Hierarchical organization is an essential characteristic of living things. Although most biologists affirm the concept of living things as hierarchically organized structures, there are widespread differences of interpretation in the meaning of hierarchy and of how the concept of hierarchy applies to living things. One such basic difference involves the distinction between the concept of control hierarchy and classification hierarchy. It is suggested that control hierarchies are distinguished from classification hierarchies in that while the former involve authority relationships between levels, the latter do not. This is illustrated in an analysis of proposed hierarchies of replicators and interactors.